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A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
Sammon mapping; Scalar field; Second derivative; Self-concordant function; Semi-differentiability; Semilinear map; Set function; List of set identities and relations; Shear mapping; Shekel function; Signomial; Similarity invariance; Soboleva modified hyperbolic tangent; Softmax function; Softplus; Splitting lemma (functions) Squeeze theorem ...
Thus metric spaces together with metric maps form a category Met. Met is a subcategory of the category of metric spaces and Lipschitz functions. A map between metric spaces is an isometry if and only if it is a bijective metric map whose inverse is also a metric map. Thus the isomorphisms in Met are precisely the isometries.
In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one which satisfies a stronger, more robust condition. A completely positive map is one which satisfies a stronger, more robust condition.
In mathematics, especially in algebraic topology, the mapping space between two spaces is the space of all the (continuous) maps between them.. Viewing the set of all the maps as a space is useful because that allows for topological considerations.
In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. [1] [2] [3] That is, a function : is open if for any open set in , the image is open in . Likewise, a closed map is a function that maps closed sets to closed sets.
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A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative integer , a multilinear map of k variables is called a k-linear map. If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.